Electric Circuits
Beginner
Current in Magnetic Field
Source: High school physics (Chinese)
Problem
A straight wire 2 m long makes an angle of $30^{\circ}$ with a uniform magnetic field of magnitude $0.050$ T. The wire carries a current of $2$ A. Find the Ampere force on the wire.
$F = 0.10$ N.
The Ampere force on a straight current-carrying segment in a uniform field is
$$F = BIL\sin\theta,$$where $\theta$ is the angle between the current direction and $\vec{B}$.
Substituting $B = 0.050$ T, $I = 2$ A, $L = 2$ m, $\theta = 30^{\circ}$:
$$F = 0.050 \times 2 \times 2 \times \sin 30^{\circ} = 0.050 \times 2 \times 2 \times 0.5 = 0.10\ \text{N}.$$The force is directed perpendicular to both the wire and $\vec{B}$, according to the left-hand rule.